Referring to professors in papers

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When referring to professors in academic papers, it is generally appropriate to use their full title, such as "Professor Xxxx Xxxxxxx, Ph.D." This format conveys respect and acknowledges their academic credentials. Using "Doctor Xxxx Xxxxxxx" is also acceptable, but "Professor" is often preferred in educational contexts. The discussion highlights the importance of professionalism in academic writing. Properly addressing professors enhances the credibility of the paper.
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This is sort of off-topic, but I couldn't find a better forum to ask in.

I'm writing a paper for my internship, and I need to refer to one of my professors for purposes of background information. I want to do this in a professional manner.

Should I say Professor Xxxx Xxxxxxx, Ph.D.?
Doctor Xxxx Xxxxxxx?
 
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I just noticed that I accidentally clicked on the math forum instead of the physics one. Feel free to move this.
 
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Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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